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Journal of Plant Pathology (2012), 94 (1), 181-191
Edizioni ETS Pisa, 2012
181
MODELS TO PREDICT THE COMBINED EFFECTS OF TEMPERATURE
AND RELATIVE HUMIDITY ON PECTOBACTERIUM ATROSEPTICUM
AND PECTOBACTERIUM CAROTOVORUM subsp. CAROTOVORUM
POPULATION DENSITY AND SOFT ROT DISEASE DEVELOPMENT
AT THE SURFACE OF WOUNDED POTATO TUBERS
A.A. Moh, S. Massart, M.H. Jijakli and P. Lepoivre
University of Liege, Gembloux Agro-Bio Tech (GxABT), Plant Pathology Unit
Passage des Déportés 2. 5030 Gembloux, Belgium
SUMMARY
INTRODUCTION
The main objectives of this study were to evaluate
and model the influence of temperature (10, 15 and
20°C), relative humidity (86, 96 and 100%) and initial
concentration of bacterial inoculum (105, 107 et 109
CFU ml-1) on the population density of Pectobacterium
atrosepticum (Pba) and Pectobacterium carotovorum subsp. carotovorum (Pcc) which are important potato
pathogens in temperate climates, and on the development of soft rot symptoms caused by these bacteria at
the surface of wounded potatoes tubers under controlled conditions. Experiments were carried out according to a Box-Behnken experimental design, simplifying prediction of the combined effects of three controlled factors. With both bacterial species, statistical
analysis showed a significant effect of temperature, relative humidity and initially applied bacterial concentration on population dynamics and soft rot development
at the surface of wounded potato tubers. Multiple regression analyses and the contour plots showed that the
temperature is the most important factor, followed by
the initially applied bacteria concentration and relative
humidity. More than 64% of the variability of the soft
rot symptoms observed could be explained by the presence of Pba and Pcc at the level of wounded potato tubers under the combined effect of tested factors. The
quadratic polynomial models developed in our research
should integrate the heterogeneity of tested bacteria belonging to the same species (which was not evaluated in
this preliminary investigation) in further research.
Pectobacterium atrosepticum (Dye 1969; Gardan et
al., 2003) (former name Erwinia carotovora subsp.
atroseptica) (Pba), Pectobacterium carotovorum subsp.
carotovorum (Dye 1969; Gardan et al., 2003) (former
name Erwinia carotovora subsp. carotovora) (Pcc) and
Dickeya spp. (Burkholder 1953; Samson et al., 2005)
(former name Erwinia chrysanthemi) are pathogenic to
potato crops (Pérombelon and Kelman, 1980). They
cause blackleg in the field and soft rot of tubers in storage (Pérombelon and Kelman, 1987; Pérombelon, 2002;
de Haan et al., 2008). These bacteria are Gram-negative, non-spore-forming, facultative anaerobes, produce
a large variety of extracellular pectic enzymes, including
pectate lyase (PEL) and pectin methyl esterase (PME),
that are major virulence factors in soft rot development
(Smadja et al., 2004).
Soft rot is a serious problem for potato production
and can cause significant economic losses during plant
growth, harvest, transport and storage (Latour et al.,
2008). The three bacteria are found on plant surfaces
and in the soil where they can penetrate potato tubers
through natural openings (lenticels) and wounds (Toth
et al., 2003). Once inside the plant, they may reside in
the vascular tissue and intercellular spaces of suberized
or parenchymatous tissues where they remain (latent
stage) until the environmental conditions, including temperature and humidity, become suitable for disease development (Pérombelon and Salmond, 1995). Macerated
tissues are wet, cream to tan in colour, with a soft, slightly granular consistency. In spite of much research, no effective chemical treatment (Diallo et al., 2009; Evans et
al., 2010) nor resistant cultivars are available for controlling potato soft rot (Rasche et al., 2006). Potato shippers
(producers and traders) need information that would enable them to predict the conditions favourable for bacterial and soft rot symptoms development.
Kendrick et al. (1959) used a temperature/relative
humidity index to predict the incidence of bacterial soft
rot on naturally infected potato tubers, but the species
and the quantity of bacteria involved in disease development were not specified. Kushalappa and Zulfiqar
(2001) tried to model soft rot of potato tubers with re-
Key words: Pectobacterium spp., temperature, relative
humidity, potato tubers, predictive microbiology.
Corresponding author: P. Lepoivre
Fax: +32.81.610126
E-mail: philippe.lepoivre@ulg.ac.be
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Modelling Pectobacterium density and soft rot disease
spect to temperature, relative humidity, and duration of
storage, but their predictive model was developed for
Pcc only. Moreover, this model did not take into account
the population level of Pcc present at the infection site.
Several studies were dedicated to ecology, epidemiology
and detection of Pectobacterium spp. infecting potato
tubers (Pérombelon and Kelman, 1980; Pérombelon,
1992; Toth et al., 1999; Diallo et al., 2009). To our
knowledge, however, no mathematical model has been
developed to describe Pectobacterium spp. and Dickeya
spp. population dynamics and symptom development
under the combined effect of the most important factors of storage environment. Although an outbreak of
Dickeya spp., known as a potato pathogen in warm regions (Pérombelon, 2002), has been reported during recent decades from western and northern Europe (Laurila et al., 2008; Toth et al., 2011), this study will focus on
Pba and Pcc, because they are associated to potato
mainly in temperate countries (Czajkowski et al., 2011).
The main aims of this work were, on one hand, the
use of a tool for the quantification of Pectobacterium
spp. populations (in order to follow bacterial population densities under various ecological conditions at the
level of wounded potato tuber) and, on the other hand,
to connect the observed bacterial population densities
with a risk factor for the development of potato tubers
soft rot.
MATERIALS AND METHODS
Biological materials. Strains used in this study (Pba
03034/1 and Pcc 030033) were isolated and characterised by the Walloon Agricultural Research Centre
(CRA-W) of Libramont (Belgium). Strains were stored
frozen at -80°C in glycerol 25% (v/v) for long-term storage and were always replicated at least twice on nutrient
agar (NA) (Difco, Belgium) before use in the experiments. A pathogenicity test was first performed by inoculating a suspension of 107 CFU ml-1 of a 2-day-old NA
culture on sterilised potato tuber slices in Petri dishes
with both bacteria (Pba 03034/1 and Pcc 030033).
Healthy tubers of the highly soft rot-susceptible cv.
Bintje, purchased from local retail stores, were washed
to remove excess soil, were surface-sterilized in 10%
sodium hypochlorite for 20 min, rinsed three times in
distilled water for 10 min and air-dried for ca. 20 min in
a laminar flow hood. Cylinders (without epidermis)
with a diameter of 12 mm and 20 mm in length, were
extracted with a cork borer from the tubers.
Culture media for plating. Four semi-selective media,
viz. CVPB (Bdliya and Langerfeld, 2005), CVPM
(Ahmed, 2001), CVP-S1 and CVP-S2 (Hyman et al.,
2001), based on crystal violet pectate, were selected
from the literature. The double layer CVP-S2 (Hyman
Journal of Plant Pathology (2012), 94 (1), 181-191
et al., 2001) was retained for assays because this medium allows a better enumeration of Pba 03034/1 and Pcc
030033 as compared to the three other media.
Controlling chamber humidity. Desiccators (miniature growth chambers) with a maximal capacity of 1
litre of water were used. The relative humidity (RH) inside desiccators was controlled using two saturated salt
solutions, KCl (86%) and KNO3 (96%) (Winston and
Bates, 1960; Lahlali et al., 2008) and distilled water
(100%). Pure salts were dissoved in 1 litre of distilled
water and stirred until a saturated solution was obtained. The resulting RH varied slightly and gradually
with the temperature (Winston and Bates, 1960). For
each temperature-humidity combination, there was one
desiccator, containing 250 ml of an appropriate saturated salt solution with excess of the solid phase of the salt
to maintain the desired RH. Desiccators with differents
humidities were incubated for 48 h at the experimental
temperature (10, 15 and 20°C) before introducing inoculated potato tubers. RH was monitored by means of a
thermohygrometer in each desiccator.
Experimental design. The Box and Behnken (1960)
experimental design (BBD) was used to check, on one
hand, the isolated and combined effect of temperature
(T), RH and initially applied bacterial concentration
(Con) on the final bacteria density at the surface of the
wounds of potato tubers, expressed as Log(CFU cm-2)
and, on the other hand, the effect on the development
of soft rot symptoms induced at the surface of the
wounded potato tubers, expressed as percentage of rotted tissue. BBD allows to studying the effects of three
factors in a single block of 15 sets of test conditions and
three central points. The order of the experiments was
fully randomized. Three levels were attributed to each
factor, coded as –1, 0, +1, so that each experiment
could be located by its three coded values (Table 1 and
2). Multiple regression analysis was carried out by using
the software package Minitab version 15 to establish a
quadratic polynomial model which would allow to predict the answer. This model had the following form:
Y = β0 + β1XT + β2XRH + β3XCon + β11(XT)2 + β22(XRH)2
+ β33(XCon)2 + β12XTXRH + β13XTXCon + β23XRHXCon
where Y is the response expressed as the logarithm of
the final bacteria density at the surface of the wounds of
potato tubers, Log(CFU cm-2) or as percentage of quantity of macerated tissue at the levels of these wounds, β0
is a constant coefficient and the regression coefficients
(β1, β2 and β3), (β11, β22, and β33) and (β12, β13, and β23)
represent, respectively, the linear, quadratic, and interaction effects of the model, estimated by multiple regression analysis. X is the coded value (between –1 and
+1) of the factor indicated by the attached subscript (T,
RH and Con). Interpretation of the data was based on
Relative
humidity (%)
Applied
concentration
(CFU ml-1)
(% of rotted tissue)
Observed values
Predicted values
Observed values
Predicted values
109
7.90 ± 0.02
7.93
13.46 ± 0.83
14.73
E2
15
96
107
7.45 ± 0.25
7.44
12.15 ± 0.66
11.81
E3
20
86
107
7.60 ± 0.09
7.52
19.70 ± 0.29
22.01
E4
10
86
107
5.84 ± 0.01
5.83
6.05 ± 0.40
5.12
E5
10
96
105
3.89 ± 0.05
3.80
3.89 ± 0.31
5.87
E6
20
100
107
7.71 ± 0.09
7.72
26.08 ± 1.25
27.01
E7
15
96
107
7.42 ± 0.27
7.44
12.12 ± 1.83
11.81
E8
20
96
109
9.49 ± 0.17
9.58
52.06 ± 1.46
50.08
E9
10
100
107
5.90 ± 0.01
5.98
7.33 ± 0.50
5.02
E10
15
100
105
5.35 ± 0.04
5.37
8.84 ± 0.43
9.17
E11
20
96
105
5.59 ± 0.23
5.57
10.67 ± 0.78
9.40
E12
15
100
109
9.70 ± 0.01
9.59
33.18 ± 2.86
34.22
E13
15
86
109
9.28 ± 0.01
9.26
31.83 ± 2.47
31.50
E14
15
86
105
5.24 ± 0.01
5.34
8.05 ± 0.06
7.00
E15
15
96
107
7.43 ± 0.16
7.44
11.17 ± 1.28
11.81
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Temperature (°C)
Symptoms
018_JPP1041RP_Lepoivre_181
Experiments
Pba population density
Log (CFU cm-2)
Journal of Plant Pathology (2012), 94 (1), 181-191
Table 1. Experimental and predicted values of population densities of Pba, expressed in log10(CFU cm-2), at the surface of potato tuber wounds and the development of soft rot at the wound surface, expressed as percentage (%) of rotted tissue.
183
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Journal of Plant Pathology (2012), 94 (1), 181-191
the signs (positive or negative effect on the response)
and statistical significance of coefficients (P<0.05). Interaction between two factors could appear as an antagonistic effect (negative coefficient) or a synergic effect
(positive coefficient). The quality of fit of the polynomial model equation was expressed by the coefficient of
determination R2.
27°C on plates that showed 30 to 300 colonies.
Preparation of the inoculum. Bacteria were plated
twice on NA before incubation overnight in 50 ml of
liquid Luria Bertani medium (LB) at 27°C with an agitation of 120 trs/min. Cells were harvested by centrifugation at 2,500 rpm for 10 min and the pellet was resuspended in sterile saline (0.85% NaCl). To determine
bacterial concentration, the optical density (OD) was
measured as the absorption at 600 nm with a Prim light
spectrophotometer 230 V (Secomam, France) and the
bacterial density of Pba and Pcc was determined by a
calibration curve according to the formula:
where P1 is the weight (g) of potato tuber cylinders inoculated before incubation, P2 is the weight (g) of cylinders inoculated after removal of the macerated tissue
with a sterile scalpel.
The quantity of the water lost (Qwl) by the cylinders
was also expressed as a percentage by the formula:
CFU ml-1 = 2 ×108 × OD600 –107
Effect of temperature, relative humidity and initially
applied inoculum on Pba 03034/1 and Pcc 030033 population densities. On each cylinder of potato tuber tissue two millipore filters (sterile support for cells applied) with a diameter of 12 mm and 0.2 µm pore size
were deposited. The bacterial suspension (20 µl) was
placed on the first filter which was not in direct contact
with potato tuber wounds for avoiding possible contaminations that could affect the quantification of bacteria
in Petri dishes. Negative control tubers were inoculated
with sterile saline (0.85% NaCl). Four potato tuber
cylinders, one of which was the negative control, were
used for each treatment, three potato tuber cylinders
representing a triplicate treatment. Groups of four
cylinders were taken from three different potato tubers.
Effect of temperature, relative humidity and initially
applied inoculum concentration on the development of
soft rot. A similar experiment as described above was
carried out with the difference that bacterial suspensions were inoculated directly on potato tuber cylinders.
To account for the loss of weight in water by cylinders
due to differents RHs inside desiccators, three non inoculated potato tuber cylinders were used for each combination tested. Desiccators containing the three types of
treatments described above were incubated at the set
temperatures (10, 15 and 20°C) for 3 days.
Counting of bacteria. At the third day of incubation,
the first filter with bacteria was removed aseptically and
suspended for ca. 10 min in Falcon tubes containing 5
ml of sterile saline. Decimal dilution-plating was done
on CVP-S2. Based on the indicatations of preliminary
trials, 100 µl suspensions were plated, which allowed
counting the bacteria after 48 or 72 h of incubation at
Quantification of macerated tissues. Three days after
incubation, two measurements were made. The quantity
of macerated tissue (Qmt) was expressed as percentage
by the formula:
Qmt (%) = P1 – P2/P1
Qwl (%) = P’1 – P’2/P’1
where P’1 is the weight (g) of non inoculated cylinders
before incubation, P’2 is the weight (g) of non inoculated cylinders after three days incubation.
Finally, Qmt and Qwl were used to estimate the net
quantity of removed macerated tissue (Qn) by the formula:
Qn (%) = Qmt – Qwl
Correlation between the population density of Pba
03034/1 and Pcc 030033 and the development of soft
rot symptoms. An analysis of the correlation between
the population density of Pba and Pcc and the development of soft rot symptoms was made with the software
package minitab version 15 (Minitab Inc. 2006, USA).
RESULTS AND DISCUSSION
Effect of temperature, relative humidity and initially
applied inoculum concentration on the population density of Pba 03034/1 and Pcc 030033 at the surface of
the wounds of potato tubers. The quadratic models describing simultaneously the effect of T, RH and Con on
the population density of both bacteria at the surface of
the wounds of potato tubers were as follows:
(1) Y1= 7.438 + 0.856XT + 0.088XRH + 2.036XCon –
0.675(XT)2 – 0.001(XRH)2 – 0.045 (XCon)2 + 0.012XTXRH
+ 0.076XTXCon + 0.07XRHXCon
(2) Y2= 6.555 + 0.379XT – 0.063XRH + 1.989XCon –
0.465(XT)2 + 0.019(XRH)2 + 0.166(XCon)2 + 0.030XTXRH
+ 0.033XTXCon + 0.019XRHXCon
where Y1 and Y2, are, respectively, the predicted population density of Pba and Pcc (Log CFU cm-2), at the
surface of the wounds. XT (temperature), XRH (relative
humidity), and XCon (initial concentration of bacteria)
are coded variables ranging from –1 to +1. The results
of observed and predicted average values of population
densities of Pba and Pcc under various ecological condi-
Relative
humidity (%)
Symptoms
(% of rotted tissue)
Observed values
Predicted values
Observed values
Predicted values
109
7.78 ± 0.03
7.83
10.30 ± 1.06
12.01
E2
15
96
107
6.59 ± 0.13
6.55
9.31 ± 1.01
9.27
E3
20
86
107
6.35 ± 0.09
6.39
16.93 ± 0.73
18.69
E4
10
86
107
5.75 ± 0.03
5.70
4.14 ± 0.17
2.68
E5
10
96
105
3.88 ± 0.02
3.92
3.01 ± 0.57
4.53
E6
20
100
107
6.53 ± 0.12
6.58
19.63 ± 1.27
21.09
E7
15
96
107
6.45 ± 0.28
6.55
9.27 ± 0.74
9.27
E8
20
96
109
8.70 ± 0.12
8.66
43.49 ± 2.04
41.97
E9
10
100
107
5.81 ± 0.03
5.76
6.43 ± 0.20
4.67
E10
15
100
105
4.79 ± 0.05
4.79
7.01 ± 0.07
7.26
E11
20
96
105
4.67 ± 0.13
4.61
8,72 ± 0.34
7.01
E12
15
100
109
8.82 ± 0.07
8.81
29.78 ± 1.08
29.85
E13
15
86
109
8.65 ± 0.02
8.65
26.53 ± 1.16
26.28
E14
15
86
105
4.70 ± 0.04
4.71
6.50 ± 0.59
6.44
E15
15
96
107
6.63 ± 0.14
6.55
9.24 ± 0.54
9.27
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Temperature (°C)
Pcc population density
Log (CFU cm-2)
018_JPP1041RP_Lepoivre_181
Experiments
Applied
concentration
(CFU ml-1)
Journal of Plant Pathology (2012), 94 (1), 181-191
Table 2. Experimental and predicted values of population densities of Pcc, expressed in log10(CFU cm-2), at the surface of potato tuber wounds and the development
of soft rot at the wound surface, expressed in percentage (%) of rotted tissue.
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Modelling Pectobacterium density and soft rot disease
tions tested are recorded respectively in Tables 1 and 2
(columns 5 and 6.) With both bacterial species, differences were slight (near zero) between the predicted and
observed values for all tested combinations.
The results of the multiple regression analysis, which
provided the estimates of the model coefficients applicable to Pba and Pcc are listed, respectively, in Tables 3
and 4 (column 3). The greater the absolute value of a
linear coefficient (β1, β2, or β3), the more important was
the influence of the corresponding factor (Box and
Draper, 1987) on predicted bacterial densities. With
both bacteria, the coefficients β1 (T) and β3 (Con) were
highly significant, and the coefficient β2 (RH) was sig-
Journal of Plant Pathology (2012), 94 (1), 181-191
nificant. These results demonstrate the importance of
tested storage factors for the control of Pba and Pcc
growth, also found by Pringle et al. (1991) and
Pérombelon and Salmond (1995). For the Pba model,
the coefficients β11, β22, and β33, describing the quadratic effect of T, RH and Con, have a highly significant effect for β11, but not for β22, and β33. All quadratic coefficients of the Pcc model appeared to be higly significant, except for coefficient β22 (quadratic effect of RH)
which was not significant. All interactions coefficients,
T x RH (β12), T x Con (β13), RH x Con (β23) were not
significant in both models. These results suggested that
the interaction effect of the tested factors does not seem
Table 3. Model coefficients and their significant effects on population densities of Pba and the development
of soft rot symptoms at the surface of the wounds of potato tubers.
Table 4. Model coefficients and their significant effects on population densities of Pcc and the development
of soft rot symptoms at the surface of the wounds of potato tubers.
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Journal of Plant Pathology (2012), 94 (1), 181-191
to influence the growth model of the two bacteria within the range of the experimental domain.
Statistical analysis of the experimental responses for
Pba and Pcc models showed that the three factors tested, strongly affect cells multiplication of Pba and Pcc at
the surface of wounded potato tubers. The sensitivity of
Pba and Pcc populations to environmental conditions
offers good prospects for integrated control. Indeed,
the knowledge of the range of environmental factors
within which the pathogens can proliferate is an important step for selecting biocontrol agents. It is known
that Pectobacterium spp. require free moisture at the site
of growth (Pringle et al., 1991) and, therefore, it could
be interesting to incorporate to the model the moisture
level observed directly at the site of bacterial growth, instead of the moisture detected in the storage atmosphere. But, in this case, this adapted method would
need an instrument to check the moisture at the site of
bacterial growth.
The coefficients of determination (R2) for the two
models constructed were calculated. When the value of
R2 is close to 1.00, the model is said statistically able to
predict the answer [log10(CFU cm-2)] at the surface of
the wounded potato tubers. In terms of percentage, the
coefficient R2 is interpreted as being the part of varia-
Moh et al.
187
tion of the answer explained by variables involved in
model conception (Box and Draper, 1987). R2 values
were 99.06 for Pba 03034/1 (Table 3) and 99.40 for Pcc
030033 (Table 4). These results mean that the observed
99.06% variation of the population density of Pba and
99.40% variation of that of Pcc, are explainable by the
models.
The contour plots describing the combined effect of
temperature and RH on the logarithm of population
densities were drawn for each inoculum concentration
from the equations for Pba (Fig. 1a, b and c) and Pcc
(Fig. 2a, b and c). These graphs show that, the logarithm of the Pba and Pcc population density increases
with the incubation temperature within the range of the
experimental data. These results indicate that the
growth of both bacteria is temperature-dependent. A
similar temperature-dependent increase in the number
of bacteria was also reported for Pba on wounded potato two days post inoculation by van Vuurde and de
Vries (1994). The increasing populations of Pba and Pcc
with temperature suggest also an increase of the risk of
soft rot initiation. As observed by several authors, when
a critical number of Pectobacterium spp. (107-108 cells)
is reached at the infection site, the bacteria produce and
secrete several extracellular enzymes including pecti-
Fig. 1. Contour plots showing the predicted effect of temperature and relative humidity, on the population density of Pba, expressed in number of log10(CFU cm-2), at the surface of the wounds of potato tubers inoculated with 105 (a), 107 (b) and 109 (c)
CFU ml-1 of Pba; and on the development of soft rot symptoms at the surface of the wounds, expressed as percentage (%) of rotted tissue, inoculated with 105 (d), 107 (e) and 109 (f) CFU ml-1 Pba.
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Journal of Plant Pathology (2012), 94 (1), 181-191
Fig. 2. Contour plots showing the predicted effect of temperature and relative humidity on the population density of Pcc, expressed in number of log10(CFU cm-2), at the surface of the wounds of potato tubers inoculated with 105 (a), 107 (b) and 109 (c)
CFU ml-1 of Pcc; and on the development of soft rot symptoms at the surface of the wounds, expressed as percentage (%) of rotted tissue inoculated with 105 (d), 107 (e) and 109 (f) CFU ml-1 Pcc.
nolytic enzymes essential for virulence (Barras et al.,
1994; Maë et al., 2001; Pérombelon 2002; Latour et al.,
2008). This production is controlled by a quorum-sensing process that relies upon the production of N-acylhomoserine lactones (HSL) (Toth et al., 2004; Cirou et al.,
2010). An increase of the risk of soft rot initiation at the
surface of wounded potato tubers could also result in an
increase of the risk of further disease development. Indeed, when the infection was initiated any further disease development was dependent on the water potential
of potato tubers (Pérombelon and Salmond, 1995;
Pérombelon, 2002). In our experiments, the growth of
Pba and Pcc was found to be more dependent on T than
on RH regardless of Con. Furthermore, the minimum
and maximum growth rate of both bacteria were found
to be 10°C and 20°C, respectively, irrespective of the
initial Pectobacterium concentration applied. We also
observed that maximum growth of Pba for the three initial concentrations were about tenfold higher than those
of Pcc. These results suggest that Pba grows more quickly than Pcc at the surface of potato tuber wounds.
In this work, population dynamics of Pectobacterium
were followed at the level of potato tuber wounds. It
would be interesting to follow Pectobacterium population dynamics in the natural openings on the tuber surface (lenticels) and population development over longer
periods of storage. But this would require an adequate
inoculation method via lenticels such as vacuum infiltration and an appropriate experimental design.
Effect of temperature, relative humidity and inoculum concentration on the development of potato tuber
soft rot symptoms. The percentage of the quantity of
macerated tissue of potato tubers at the wound level
due to bacteria and combined effect of T, RH and Con
was predicted by the following quadratic polynomial
equations:
(3) Y3= 11.814 + 9.721XT + 1.225XHR + 12.386XCon +
1.261(XT)2 + 1.715(XHR)2 + 6.944(XCon)2 +
1.276XTXHR + 7.955XTXCon + 0.137XHRXCon
(4) Y4= 9.272 + 8.109XT + 1.095XHR + 10.609XCon +
0.717(XT)2 + 1.794(XHR)2 + 1.35(XCon)2 + 0.102XTXHR
+ 6.869XTXCon + 0.686XHRXCon
where Y3 and Y4 represent, respectively, the predicted
percentages of the quantity of rotted of potato tuber tissues by Pba and Pcc; X, is the coded values (between -1
and +1) of the factor indicated by the attached subscript (T, RH and Con). The results of measuring and
predicting percentage of rotted tissue at the wound level are presented in Tables 1 and 2 (columns 7 and 8).
There is no substantial difference between the observed
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Journal of Plant Pathology (2012), 94 (1), 181-191
and predicted percentage of rotted tissue at the surface
of wounded potato tubers caused by each tested bacterium (Pba and Pcc).
Tables 3 and 4 (columns 4 and 4, respectively) summarize the estimated regression coefficients given by the
multiple regression analysis. All linear coefficients of
both models, β1, β2, and β3 which represent, respectively, the linear effects of T, RH and Con, are highly significant for β1 and β3 but only significant for β2. These results are in accordance with the data reported by Togbé
(2007) on soft rot development in potato tubers slices
inoculated with Pba.
Several authors have pointed out the importance of
each factor separately on disease development by Pba
and Pcc (Pérombelon and Kelman, 1980; Pérombelon,
1992; Kushalappa and Zulfiqar, 2001). The coefficients
β11, β22, and β33 which describe the quadratic effect of
T, RH and Con for the Pba and Pcc model were, respectively, not significant, significant and highly significant.
The interactions T x RH and RH x Con were not significant for the two models. Quadratic or interaction effect
of those factors that were not significant, appear to suggest that they did not influence the percentage of rotted
tissue predicted by each model in our conditions, contrary to those that were significant. Latent infection of
potato tubers by Pectobacterium spp. is widespread
(Pérombelon, 2002; Toth et al., 2003) and if high RH
(85 to 95%) is applied to storage rooms (Martin and
Gravoueille, 2001) so that the interaction RH x Con is
significant, massive cases of sot rot development in storage rooms can be expected at the surface of wounded
potato tubers. The combined effect of T x Con was positive and very highly significant in both models. These
results suggest a synergistic effect of this combination
on the maceration of potato tubers. R2 values show that
T, RH and Con account for 97.63% (Table 3) and
97.00% (Table 4) of the percentage of rotted tissue variation observed in the Pba and Pcc model, respectively.
The contour plots showing the combined effect of T
and RH on the percentage of potato tubers diseased at
the wound level were also drawn for each bacterium
concentration from the model for Pba (Fig. 1d, e and f)
and Pcc (Fig. 2d, e and f). The choice of each bacterium
concentration for contour plots construction was based
on the fact that the quantity of initial inoculum present
on potato tubers at the time of storage was fixed,
whereas the two other ecological factors (T and RH)
varied. With reference to the Pba and Pcc growth observed in this study, the percentage of diseased potato
tubers seemed to depend more on T than RH, regardless of Con. Togbé (2007) obtained similars results with
Pba on potatoes tubers slices. Moreover, the highest
percentage of potato tuber tissue diseased by Pba and
Pcc was observed when T and RH were highest (20°C
and 100%) with a more important value for Pcc, independently of the the initial bacterial concentration used.
Moh et al.
189
These results suggest that Pcc produced more soft rot
than Pba in our experimental conditions. The differential effect of temperature on the pathogenic behaviour
of Pba and Pcc may be attributed to its effect on pectate
lyase production (Smadja et al., 2004).
All polynomial models described in this investigation
with multi-factorial analysis are valid only within the experimental domain of the tested key environmental factors, for the Pectobacterium strains employed and the
potato cv. Bintje (Kushalappa and Zulfiqar, 2001; Lui
and Kushalappa, 2003).
The modelling approach chosen for this study was
the “response surface methodology” (RSM) applied to
the Box and Behnken (1960) experimental design. RSM
is a mathematical approach most often used to describe
the simultaneous effect of several factors on microbial
behaviour (Delignette-Muller, 2009; Moh et al., 2011).
BBD, an experimental design of RSM, was preferred
because relatively few experimental combinations of the
variables are adequate to estimate complex response
functions. BBD has been widely used to predict the
growth of food-borne pathogens (Sautour et al., 2003;
Lahlali et al., 2008) or plant pathogens (Togbé et al.,
2007) in relation to at least three environmental factors.
Correlation between the population density of Pba
03034/1 and Pcc 030033 and the development of soft
rot symptoms. Analysis of the correlation between the
population densities of Pectobacteria and the development of potato tuber soft rot shows a linear coefficient
of correlation (r) equal to 0.83 (R2 = 69%) and 0.80 (R2
= 64%) for Pba and Pcc, respectively. These results indicate that more than 64% of the variability of soft rot
symptoms observed could be explained by the presence
of Pba and Pcc at the level of wounded potato tubers
with the combined effect of T, RH and Con. The combined effect of these factors, however, may not be the
only incitant of soft rot development at the surface of
wounded potato tubers. Other factors that were not
controlled in the experiment, such as the O2 status in
the dessicator, the physiological resistance of the cultivar used, the harvesting, or the storage conditions of the
tuber could also interfere with disease development
(Kushalappa and Zulfiqar, 2001; Lui and Kushalappa,
2003). Moreover, the growth behaviour of the tested
bacteria on a non natural growth support (millipore)
would not be the same if they were grown directly on
potato tubers tissue.
In conclusion, this work constitutes a preliminary
study addressing the evaluation and modelling the influence of T, RH and Con on the population dynamics of
Pba and Pcc, and on the development of soft rot symptoms caused by these bacteria at the surface of wounded
potatoes tubers. The four models developed in this study
had a good capacity of response prediction (R2 value is
close to 1.00 for each model). However, for using these
018_JPP1041RP_Lepoivre_181
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Modelling Pectobacterium density and soft rot disease
models as warning systems to make management decisions, some adaptations to practical conditions involving
different strains of bacteria, potato cultivars, physiology
of potato tubers, harvesting and storage conditions are
required. All polynomial models developed in this investigation did not include the heterogeneity of the tested
bacteria belonging to the same species. This is why further research should take into consideration the large genetic variation within the genus Pectobacterium (Pba and
Pcc) and Dickeya spp. that were isolated from potatoes in
western and northern Europe during recent years. In
this investigation the risk factor of disease development
was qualitative i.e. a low or high Pectobacterium population corresponded respectively to a low or high risk of
disease development. It could be interesting to quantify
this risk factor i.e. associate qualitative risk (low or high)
of soft rot development with the number of potato tubers diseased (disease incidence). To better approximate
naturals conditions of soft rot development further study
should also be conducted on entire potato tubers inoculated at the lenticel level.
ACKNOWLEDGEMENTS
We thank Mr. J.L. Rolot from Walloon Agricultural
Research Centre (CRA-W), Libramont (Belgium) for
kindly supplying the strains of Pectobacterium spp. and
Mr. O. Dutrecq and R. Lahlali, respectively, for the protocol used for bacteria enumeration and for assistance
and helpful discussion. Special thanks to Mr. Y.
Brostaux from the unity of Applied Statistics, Computer
Science and Mathematics (SIMa) of the University of
Liege, Gembloux Agro-Bio Tech (GxABT) for the excellent assistance with statistical analysis. Finally, the
senior author thanks the Government of the Côte
d’Ivoire for the scholarship.
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